Eureka!

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A mathematical problem older than most students has been solved by a Victoria University Professor.

40 years after the problem was conceived, Professor Geoff Whittle of the School of Mathematics, Statistics and Operations Research has solved the problem known as ‘Rota’s Conjecture’ with professors from Canada and the Netherlands. Whittle has been working on the problem for the past 15 years.

“It’s a little bit like discovering a new mountain—we’ve crossed many hurdles to reach a new destination and we have returned scratched, bloodied and bruised from the arduous journey,” said Whittle, adding that though the Conjecture has been solved, it will take hundreds of pages to write up the results of his work.

The conjecture was posed by famous mathematician and philosopher Gian-Carlo Rota in 1970. It relates to the matroid theory, which investigates geometric structures that can be completely different from those in our world. Rota’s Conjecture is a way of using mathematics to recognise these alternative structures.

“I like to compare it to Kafka’s Metamorphosis story, where a man wakes up and realises he has transformed into an insect—the way he views the world changes entirely.

“Matroid theory is all about visualising a world of new geometrical structures and developing ways of describing the big, overarching structures which would emerge.”

Professor Whittle’s success comes after 21 years in Victoria’s mathematical department, a research fellowship at Oxford University, his investment as a Fellow into the Royal Society of New Zealand, and the achievement of the New Zealand Mathematical Society’s Research Award.

Head of School Dr Peter Donelan is delighted with Whittle’s achievement, calling it “one of the outstanding mathematical achievements in recent years”.

While it is indeed a great success, the professors still have several years of work ahead of them as they document their results so others can follow the pathway they took to solving the decades-old problem.

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